Single-Anchor Graph-Spectral Manifold Adaptation for Near-Field Underwater Bearing Estimation

Large-aperture hydrophone arrays at short ranges require spherical steering to represent wavefront curvature. After modeling this propagation, residual mismatch remains, and one imperfect reference observation provides limited evidence about which components will transfer reliably. We propose graph-spectral manifold adaptation for near-field bearing estimation (GSMA-NF), combining a geometry-derived spherical manifold and a physical sensor graph to constrain single-anchor residual transfer. GSMA-NF removes nominal spherical propagation from the anchor observation, represents the residual in the graph Fourier basis, and uses high-order energy as an uncertainty proxy to attenuate weakly supported low-order modes. Range-profiled multiple signal classification (MUSIC) estimates bearing with the adapted manifold, while an independent covariance rank-dominance criterion controls output release. Controlled simulations show that spherical modeling reduces short-range plane-wave error and that adaptive shrinkage limits severe negative transfer under weak-anchor conditions, while fixed graph smoothing provides comparable performance in several conditions. Model-mismatch and directional-transfer tests relate graph-prior benefit to low-order residual structure and bearing offset; interference tests delimit rank dominance to output-support assessment. Lake data show stable nominal-frame bearings across contiguous windows of a narrowband fixed-source sequence, while the screen withholds a window with insufficient rank dominance, supporting fixed-source temporal transfer in the nominal array frame.